Energy and angular dependences of the elastic and inelastic scattering of electrons from H 2 and CO have been measured in the energy range from 0. 5 eV to 10 eV and for scattering angles ranging from 5 to 110°. The elastic cross sections are composed of potential and resonance scattering and therefore are difficult to interpret. The excitation of molecular vibrations, i.e., scattering into inelastic channels, contains predominant contributions from short-lived negative ion compound states. The qualitative agreement of the measured angular dependence with that predicted from pure resonant scattering considerations is shown to be able to fix certain symmetry quantum numbers of the molecular state. Moreover, characteristic and similar cr-, 7r-, A-. .. type angular dependences throughout the whole energy range of the molecular resonance (independent of the final vibrational state) are presented as a means of verifying the presence of a resonance, even when the short lifetime masks the usually characteristic resonant peaks. The half-width of the CO~~27r state is about 0.4 eV, that for H 2 2 2 M between 2 and 4 eV. Absolute total cross sections for the different inelastic channels are given. The resonances of N 2 , CO, and H 2 are compared*with the predictions of the single-particle-shape resonance model and their physical properties are discussed using the different potential energy terms at large distances between the additional electron and the molecule. Throughout, stress is laid on the importance of choosing the proper experiment (i.e., exit channel) when one wishes to study a resonance. Predictably, in using angular dependence, certain channels hide and others exhibit the presence of the resonance.The existence of short-lived negative ion states, formed in the scattering of low-energy electrons with molecules, has been established in several papers experimentally as well as theoretically. For this purpose measurements have been made of the: i, energy dependence of the attenuation of an electron beam after passing through a gas-filled scattering chamber, 1 " 3 ii, the energy dependence of the elastic and inelastic scattering cross section in the forward direction or into different scattering angles, 4 "" 8 and iii, the energy dependence of the total cross section for the dissociative attachment process. 9 ' 10 In certain energy ranges resonances are seen (methods i and ii), i.e. , considerable changes of the cross sections, which indicate compound states, if the variation of the wavelength of the colliding electrons in this energy range is small compared with the dimensions of the scatterer. This excludes diffraction effects as a reason for the cross section changes. Near the resonance energy, the cross section may increase and/or decrease, depending on the values of two scattering phases. The first is the phase of the outgoing electron wave of the direct collision process with the molecule M M+e-~Mj* + e, and the second, the value of the phase of the one (spherical for atoms, spheroidal for diatomics) partial wav...